Question

If the point P(m, 3) lies on the line segment joining the points A(-2/5,6) and B(2, 8), then the

value of m is.....



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Answer 1

Answer:

The value of m is -4.

Step-by-step explanation:

If the point P(m,3) lies on the line segment joining the point A(-2/5,6),and B(2,8), then all these points are collinear and the slopes AB, AP, PB are same.

Slope formula:

m=\frac{y_2-y_1}{x_2-x_1}m=

x

2

−x

1

y

2

−y

1

Slope of AB is

m_1=\frac{8-6}{2+\frac{2}{5}}=\frac{2}{\frac{12}{5}}=\frac{5}{6}m

1

=

2+

5

2

8−6

=

5

12

2

=

6

5

The slope of PB is

m_2=\frac{8-3}{2-m}=\frac{5}{2-m}m

2

=

2−m

8−3

=

2−m

5

m_1=m_2m

1

=m

2

\frac{5}{6}=\frac{5}{2-m}

6

5

=

2−m

5

2-m=62−m=6

2-6=m2−6=m

-4=m−4=m

Therefore the value of m is -4.

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